// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/QR>

template<typename MatrixType>
void
householder(const MatrixType& m)
{
	static bool even = true;
	even = !even;
	/* this test covers the following files:
	   Householder.h
	*/
	Index rows = m.rows();
	Index cols = m.cols();

	typedef typename MatrixType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;
	typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
	typedef Matrix<Scalar, internal::decrement_size<MatrixType::RowsAtCompileTime>::ret, 1> EssentialVectorType;
	typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
	typedef Matrix<Scalar, Dynamic, MatrixType::ColsAtCompileTime> HBlockMatrixType;
	typedef Matrix<Scalar, Dynamic, 1> HCoeffsVectorType;

	typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::RowsAtCompileTime> TMatrixType;

	Matrix<Scalar, EIGEN_SIZE_MAX(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime), 1> _tmp(
		(std::max)(rows, cols));
	Scalar* tmp = &_tmp.coeffRef(0, 0);

	Scalar beta;
	RealScalar alpha;
	EssentialVectorType essential;

	VectorType v1 = VectorType::Random(rows), v2;
	v2 = v1;
	v1.makeHouseholder(essential, beta, alpha);
	v1.applyHouseholderOnTheLeft(essential, beta, tmp);
	VERIFY_IS_APPROX(v1.norm(), v2.norm());
	if (rows >= 2)
		VERIFY_IS_MUCH_SMALLER_THAN(v1.tail(rows - 1).norm(), v1.norm());
	v1 = VectorType::Random(rows);
	v2 = v1;
	v1.applyHouseholderOnTheLeft(essential, beta, tmp);
	VERIFY_IS_APPROX(v1.norm(), v2.norm());

	// reconstruct householder matrix:
	SquareMatrixType id, H1, H2;
	id.setIdentity(rows, rows);
	H1 = H2 = id;
	VectorType vv(rows);
	vv << Scalar(1), essential;
	H1.applyHouseholderOnTheLeft(essential, beta, tmp);
	H2.applyHouseholderOnTheRight(essential, beta, tmp);
	VERIFY_IS_APPROX(H1, H2);
	VERIFY_IS_APPROX(H1, id - beta * vv * vv.adjoint());

	MatrixType m1(rows, cols), m2(rows, cols);

	v1 = VectorType::Random(rows);
	if (even)
		v1.tail(rows - 1).setZero();
	m1.colwise() = v1;
	m2 = m1;
	m1.col(0).makeHouseholder(essential, beta, alpha);
	m1.applyHouseholderOnTheLeft(essential, beta, tmp);
	VERIFY_IS_APPROX(m1.norm(), m2.norm());
	if (rows >= 2)
		VERIFY_IS_MUCH_SMALLER_THAN(m1.block(1, 0, rows - 1, cols).norm(), m1.norm());
	VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m1(0, 0)), numext::real(m1(0, 0)));
	VERIFY_IS_APPROX(numext::real(m1(0, 0)), alpha);

	v1 = VectorType::Random(rows);
	if (even)
		v1.tail(rows - 1).setZero();
	SquareMatrixType m3(rows, rows), m4(rows, rows);
	m3.rowwise() = v1.transpose();
	m4 = m3;
	m3.row(0).makeHouseholder(essential, beta, alpha);
	m3.applyHouseholderOnTheRight(essential.conjugate(), beta, tmp);
	VERIFY_IS_APPROX(m3.norm(), m4.norm());
	if (rows >= 2)
		VERIFY_IS_MUCH_SMALLER_THAN(m3.block(0, 1, rows, rows - 1).norm(), m3.norm());
	VERIFY_IS_MUCH_SMALLER_THAN(numext::imag(m3(0, 0)), numext::real(m3(0, 0)));
	VERIFY_IS_APPROX(numext::real(m3(0, 0)), alpha);

	// test householder sequence on the left with a shift

	Index shift = internal::random<Index>(0, std::max<Index>(rows - 2, 0));
	Index brows = rows - shift;
	m1.setRandom(rows, cols);
	HBlockMatrixType hbm = m1.block(shift, 0, brows, cols);
	HouseholderQR<HBlockMatrixType> qr(hbm);
	m2 = m1;
	m2.block(shift, 0, brows, cols) = qr.matrixQR();
	HCoeffsVectorType hc = qr.hCoeffs().conjugate();
	HouseholderSequence<MatrixType, HCoeffsVectorType> hseq(m2, hc);
	hseq.setLength(hc.size()).setShift(shift);
	VERIFY(hseq.length() == hc.size());
	VERIFY(hseq.shift() == shift);

	MatrixType m5 = m2;
	m5.block(shift, 0, brows, cols).template triangularView<StrictlyLower>().setZero();
	VERIFY_IS_APPROX(hseq * m5, m1); // test applying hseq directly
	m3 = hseq;
	VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating hseq to a dense matrix, then applying

	SquareMatrixType hseq_mat = hseq;
	SquareMatrixType hseq_mat_conj = hseq.conjugate();
	SquareMatrixType hseq_mat_adj = hseq.adjoint();
	SquareMatrixType hseq_mat_trans = hseq.transpose();
	SquareMatrixType m6 = SquareMatrixType::Random(rows, rows);
	VERIFY_IS_APPROX(hseq_mat.adjoint(), hseq_mat_adj);
	VERIFY_IS_APPROX(hseq_mat.conjugate(), hseq_mat_conj);
	VERIFY_IS_APPROX(hseq_mat.transpose(), hseq_mat_trans);
	VERIFY_IS_APPROX(hseq * m6, hseq_mat * m6);
	VERIFY_IS_APPROX(hseq.adjoint() * m6, hseq_mat_adj * m6);
	VERIFY_IS_APPROX(hseq.conjugate() * m6, hseq_mat_conj * m6);
	VERIFY_IS_APPROX(hseq.transpose() * m6, hseq_mat_trans * m6);
	VERIFY_IS_APPROX(m6 * hseq, m6 * hseq_mat);
	VERIFY_IS_APPROX(m6 * hseq.adjoint(), m6 * hseq_mat_adj);
	VERIFY_IS_APPROX(m6 * hseq.conjugate(), m6 * hseq_mat_conj);
	VERIFY_IS_APPROX(m6 * hseq.transpose(), m6 * hseq_mat_trans);

	// test householder sequence on the right with a shift

	TMatrixType tm2 = m2.transpose();
	HouseholderSequence<TMatrixType, HCoeffsVectorType, OnTheRight> rhseq(tm2, hc);
	rhseq.setLength(hc.size()).setShift(shift);
	VERIFY_IS_APPROX(rhseq * m5, m1); // test applying rhseq directly
	m3 = rhseq;
	VERIFY_IS_APPROX(m3 * m5, m1); // test evaluating rhseq to a dense matrix, then applying
}

EIGEN_DECLARE_TEST(householder)
{
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(householder(Matrix<double, 2, 2>()));
		CALL_SUBTEST_2(householder(Matrix<float, 2, 3>()));
		CALL_SUBTEST_3(householder(Matrix<double, 3, 5>()));
		CALL_SUBTEST_4(householder(Matrix<float, 4, 4>()));
		CALL_SUBTEST_5(householder(
			MatrixXd(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_6(householder(
			MatrixXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_7(householder(
			MatrixXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE), internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
		CALL_SUBTEST_8(householder(Matrix<double, 1, 1>()));
	}
}
